Video Set Introduction

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Before watching the videos, think about and answer these questions to the best of your ability.

Questions 1 - 3 refer to the following context:

Madison decides to go for a run before school. She starts her run from home. The function $y = v(t)$ expresses the relationship between Madison’s velocity (in meters per minute) as she runs and the number of minutes $t$ elapsed since she started running.

What does the product $v(t) \times \Delta t$ approximate?

The average rate of change of Madison’s velocity over a particular $\Delta t$ interval. Madison’s acceleration over a particular $\Delta t$ interval. The change in Madison’s distance away from home over a particular $\Delta t$ interval. Madison’s distance away from home after having run for $\Delta t$ minutes. Madison’s instantaneous velocity at a particular moment in time.

What does the area of the blue rectangle on the graph of the function $y = v(t)$ below represent?

Madison’s average velocity over the interval of time from $t = 3$ to $t = 4$ . Madison’s distance away from home 3 minutes after she started running. The velocity at which Madison runs over the interval of time from $t = 3$ to $t = 4$ . Madison’s acceleration over the interval of time from $t = 3$ to $t = 4$ . The change in Madison’s distance away from home over the interval of time from $t = 3$ to $t = 4$ .

What does the sum $v(0) \times \dfrac {1}{2} + v\left (\dfrac {1}{2}\right ) \times \dfrac {1}{2} + v(1) \times \dfrac {1}{2} + v\left (\frac {3}{2}\right ) \times \dfrac {1}{2} + v(2) \times \dfrac {1}{2} + v\left (\frac {5}{2}\right ) \times \dfrac {1}{2}$ approximate?

Madison’s distance away from home after having run for 2.5 minutes. The average rate of change of Madison’s velocity over the interval of time from $t = 0$ to $t = \dfrac {5}{2}$ . The change in Madison’s distance away from home over the interval of time from $t = 0$ to $t = 6$ . Madison’s distance away from home after having run for 6 minutes. Madison’s acceleration over the interval of time from $t = 0$ to $t = 6$ .